function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
%   parameter for logistic regression and the gradient of the cost
%   w.r.t. to the parameters.

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
%
% Note: grad should have the same dimensions as theta
%
predic1 = zeros(size(y));
predic2 = zeros(size(y));
temp1 = zeros(size(y));
temp2 = zeros(size(y));

predic1 = X * theta;
predic2 = sigmoid(predic1); %temp = g(theta' * X)
temp1 = log(predic2);    %log(h)  ;
temp2 = log(1 - predic2);%log(1-h);
J = (1.0 / m) * (-y' * temp1 - (1-y)' * temp2);
grad = (1.0/m) * X' * (predic2 - y);





% =============================================================

end
